Inverse pseudo orbit tracing property for robust diffeomorphisms
| Autor: | Lee, Manseob |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $M$ be a closed smooth Riemannian manifold $M$, and let $f:M\to M$ be a diffeomorphism. Herein, we demonstrate that (i) if $f$ has the $C^1$ robustly inverse shadowing property on the chain recurrent set $\mathcal{CR}(f)$, then $\mathcal{CR}(f)$ is hyperbolic and (ii) if $f$ has the $C^1$ robustly inverse shadowing property on a nontrivial transitive set $\Lambda\subset M$, then $\Lambda$ is hyperbolic for $f$. Especially, the item (ii) is a proof of the conjecture of Lee and Lee \cite{LL}. Comment: 21 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|